What does this involve in the UN as part of the final recruitment process?

UNDSS (UN Department of Safety and Security) deals with Security Clearance (as a policy maker), Other UN Organisation may have their own department for safety and security but they all are obliged to abide by the UNDSS protocols.

There are various reasons for SC (administrative/facility access/restricted area access/travel/etc). Now I do not know your personal situation (origin/organization/level/assignment/duty station/etc) so I will only brief you about the 'travel'.

Security Clearance (SC) - Travel:

The UN employees referred as Travellers/Personnel while on official travel, always require a Security Clearance before they travel. SC-Travel is categorized from (1 - 6) based on geographical regions/safety/security. Basic reason for SC is to safeguard all the UN personnel traveling officially. There is nothing in it to be alarmed but it is a routine process, UN asks for travel Itineraries and basic details so they are aware of your movements (if you deviate from your said itinerary, you alarms the bell of something is not right, this may sound laughable to those with lack of exposure to the world outside of the bubble we lives in but this is how the UN safeguard their assets).